Need help designing a board game

My idea would be kind of like Trivial Pursuit, but instead of questions based on knowing stuff (in this case trivia) they would be based on reasoning stuff. Players would not only have to answer the question, but also give their reasoning for it. There would be a few more very interesting elements to the game, based precisely on having to reason out the question (but I will keep them for myself).

Here are two examples of the kind of questions that could be asked:

"Take the first N prime numbers. Multiply them and add 1. Is the result also a prime number?"

"In chess, is it possible that you end up with both your bishops on same-colored squares?"

Then the players would be required to give full explanations of their answers:

"Not necessarily. It could be a composite number that factors to primes that are not in the first N primes. For example: 2 * 3 * 5 * 7 * 11 * 13 = 30,031 = 59 * 509"

"Yes it is. It could be that one of your bishops gets taken during the game, but then you manage to promote a pawn to another bishop, which happens to be on the same-colored squares as your other bishop."

Obviously I'm assuming that the players know what primes are and how to play chess, but don't worry about that. The point I'm trying to make is that to answer the question correctly, you need to make some kind of reasoning.

I need help creating the content of the game, that is the questions. The main problem I have is that the only discipline I can think of that is suitable for this game is mathematics (I thought about creating a Miscellany category where all the chess questions would go). Science, history, literature, etc all have the problem that the questions would be knowledge-based:

"Why do boats float?" "Why did the Egyptians build the Pyramids?" "Why did Don Quixote attack the windmills?"

1) Is it possible to ask questions that require reasoning in disciplines other than mathematics and miscellany (aka chess)?

2) Would you like to contribute questions to my game? Bonus points if they are somewhat tricky.